1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the properties of earth formations. More specifically, the invention is related to methods for correcting measurements made by multi-component induction or propagation sensors for shoulder bed and borehole effects.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that when properly interpreted are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p.148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
A limitation to the electromagnetic induction resistivity well logging instruments known in the art is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones which are typically hydrocarbon-bearing and are of the most interest to the instrument user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art.
U.S. Pat. No. 5,999,883 issued to Gupta et al, (the xe2x80x9cGupta patentxe2x80x9d), the contents of which are fully incorporated here by reference, discloses a method for determination of the horizontal and vertical conductivity of anisotropic earth formations. Electromagnetic induction signals induced by induction transmitters oriented along three mutually orthogonal axes are measured. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to a one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of the perpendicular one of the orthogonal axes is calculated from the receiver signals measured perpendicular to the instrument axis. An intermediate measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation. A relative angle of inclination of one of the orthogonal axes which is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to a direction of the vertical conductivity. The rotated magnitudes are rotated through a negative of the angle of inclination. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second step of rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second step of rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter.
Shoulder bed corrections related to the effect of formations above and below the depth being evaluated also have to be applied to the data. Methods for making these corrections to data acquired with conventional logging tools are well known in the art.
For example, U.S. Pat. No. 5,446,654 to Chemali teaches the conversion of a resistivity log as a function of well depth into a rectangularized curve so that the interfaces of the adjacent strata are located, and by a suitable number of iterations, a correction factor is applied. The corrected rectangular log is obtained with a correction coefficient computed at each depth. For each computation, the impact of all the strata within a specified depth window is considered, while strata beyond that window are simplified by representing the strata beyond the window with single equivalent bed values to reduce the number of computations required. This then provides a resistivity log which is substantially free of shoulder bed effect.
The method of U.S. Pat. No. 5,867,806 to Strickland et al. selects one or more control depths at one or more locations of each of a plurality of detected beds in the formation. The method then estimates the resistivity of each bed only at the selected control depths to produce an estimated resistivity of the beds. The method then computes a simulated log value at each control depth using a current estimate of the resistivity of the beds. The computed simulated log is then compared to the actual log data at each control depth, and the resistivity of each bed is adjusted using the difference between the actual and simulated values at the control depths. The above method iteratively repeats a plurality of times until the simulated log substantially matches the actual log at the control depths.
There is a need for a method of shoulder bed correction of multicomponent resistivity data so as to improve the estimated horizontal and vertical formation resistivities obtained by inversion of the shoulder-bed corrected data. Such a method should preferably computationally efficient so as to provide the necessary corrections at the wellsite and in real time. The present invention satisfies this need.
The present invention is a method for determining an applying shoulder bed corrections to logging measurements made with a transverse induction logging tool. Layer boundaries are determined from the measurements. These are combined with horizontal and vertical resistivities obtained by a whole space anisotropic inversion to give a layered model. Preferably, a Lanczos iterative procedure is used for the inversion. The shoulder bed correction for each layer is derived based upon a difference between a 1-D synthetic response of the model and a whole space response of the model at that layer. The shoulder bed correction is applied to the data and the inversion procedure is repeated. This procedure is repeated in an iterative manner until a difference between the shoulder bed corrected measurements at the center of each of the layers and a synthetic response to a whole space model at the center of each of the layers is below a predetermined threshold.